I have bought (sold, traded) about a dozen road bikes from the 1980's. If you find one from that era that is in good shape, it makes an enjoyable bike to ride. BUT, they are only a "good deal" if you leave them as original as possible.
Just have your shop put some grease where grease is needed, replace the shifting and brake cables if necessary, adjust the shifters and brakes, replace the broken spokes, and true the wheels. Get some new 27 inch tires (Continental and Bontrager have some nice ones). Depending on how much work your shop does, you will spend about $100 or less to get the bike running as good as new. But, don't spend anymore than that.
There are LOTS of '80's bikes available that are in good riding condition. So it is not a good use of your money to spend a ton of dough on a bike with problems. (Unless it is a "Made in USA" Paramount, or something of that quality).
If you attempt the so-called "upgrade" process, with new wheels, new shifters, etc., etc., you can easily spend a bunch of money. And, it will not ride a bit better than if you had spend just $100 or so. Newer components don't make a bike "better". Just more expensive.